Del 64 - London Mathematical Society Student Texts

A Short Course on Banach Space Theory

Häftad, Engelska, 2004

AvN. L. Carothers,Ohio) Carothers, N. L. (Bowling Green State University

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This is a short course on Banach space theory with special emphasis on certain aspects of the classical theory. In particular, the course focuses on three major topics: the elementary theory of Schauder bases, an introduction to Lp spaces, and an introduction to C(K) spaces. While these topics can be traced back to Banach himself, our primary interest is in the postwar renaissance of Banach space theory brought about by James, Lindenstrauss, Mazur, Namioka, Pelczynski, and others. Their elegant and insightful results are useful in many contemporary research endeavors and deserve greater publicity. By way of prerequisites, the reader will need an elementary understanding of functional analysis and at least a passing familiarity with abstract measure theory. An introductory course in topology would also be helpful; however, the text includes a brief appendix on the topology needed for the course.

Produktinformation

Utgivningsdatum2004-12-06
Mått151 x 229 x 11 mm
Vikt300 g
FormatHäftad
SpråkEngelska
SerieLondon Mathematical Society Student Texts
Antal sidor198
FörlagCambridge University Press
ISBN9780521603720

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Preface; 1. Classical Banach spaces; 2. Preliminaries; 3. Bases in Banach spaces; 4. Bases in Banach spaces II; 5. Bases in Banach spaces III; 6. Special properties of C0, l1, and l∞; 7. Bases and duality; 8. Lp spaces; 9. Lp spaces II; 10. Lp spaces III; 11. Convexity; 12. C(K) Spaces; 13. Weak compactness in L1; 14. The Dunford-Pettis property; 15. C(K) Spaces II; 16. C(K) Spaces III; A. Topology review.

'This lively written text focuses on certain aspects of the (neo-) classical theory of Banach spaces as developed in the 1950s and 1960s and is intended as an introduction to the subject, e.g., for future Ph.D. students. … This slim book is indeed very well suited to serve as an introduction to Banach spaces. Readers who have mastered it are well prepared to study more advanced texts such as P. Wojtaszczyk's Banach Spaces for Analysts (Cambridge University Press, second edition) or research papers.' Zentralblatt MATH

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